# What is the midpoint between B(3, -5, 6) and H(5,3,2)?

Oct 18, 2017

See a solution process below:

#### Explanation:

The formula to find the mid-point of a line segment give the two end points is:

$M = \left(\frac{\textcolor{red}{{x}_{1}} + \textcolor{b l u e}{{x}_{2}}}{2} , \frac{\textcolor{red}{{y}_{1}} + \textcolor{b l u e}{{y}_{2}}}{2} , \frac{\textcolor{red}{{z}_{1}} + \textcolor{b l u e}{{z}_{2}}}{2}\right)$

Where $M$ is the midpoint and the given points are:

$\left(\textcolor{red}{{x}_{1}} , \textcolor{red}{{y}_{1}} , \textcolor{red}{{z}_{1}}\right)$ and $\left(\textcolor{b l u e}{{x}_{2}} , \textcolor{b l u e}{{y}_{2}} , \textcolor{b l u e}{{z}_{2}}\right)$

Substituting gives:

${M}_{B H} = \left(\frac{\textcolor{red}{3} + \textcolor{b l u e}{5}}{2} , \frac{\textcolor{red}{- 5} + \textcolor{b l u e}{3}}{2} , \frac{\textcolor{red}{6} + \textcolor{b l u e}{2}}{2}\right)$

${M}_{B H} = \left(\frac{8}{2} , - \frac{2}{2} , \frac{8}{2}\right)$

${M}_{B H} = \left(4 , - 1 , 4\right)$

Oct 18, 2017

(4,-1,4)

#### Explanation:

for each of the corresponding x, y, and z coordinates:
-find the difference between them
- divide that difference by 2
- add to that coordinate for point B.

...for the x coordinate, you have $\frac{5 - 3}{2} + 3$, so the x coordinate is 4. (4 is halfway between 3 and 5).

y coordinate: $\frac{3 - \left(- 5\right)}{2} + \left(- 5\right) = - 1$ (-1 is halfway betwwen -5 and 3)

z coordinate: $\frac{2 - 6}{2} + 6 = 4$ (4 is halfway between 6 and 2)

GOOD LUCK

Oct 18, 2017

The midpoint is: $\left(4 , - 1 , 4\right)$

#### Explanation:

The midpoint between two points, $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ is:

$\left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2} , \frac{{z}_{1} + {z}_{2}}{2}\right)$

Applying this to the two given points:

$\left(\frac{3 + 5}{2} , \frac{- 5 + 3}{2} , \frac{6 + 2}{2}\right)$

$\left(4 , - 1 , 4\right)$